The choice of \(N_{}=2\) 
which characterizes the ISP Hermitization of Ref. [1]}
can be generalized.
The number \(N_{}\)  of the auxiliary,
manifestly unphysical
inner-product spaces \({\cal R}_j\)  with \(j> 0\,\) 
can be,
in the resulting
GSP extension of the ISP formulation of quantum mechanics,
arbitrarily large.
The ISP triplet
(REF ) of the inner-product spaces
sharing the same ket-vector elements of \({\cal V}\) 
will be replaced by the \(K-\) plet
\(\lbrace {\cal H}_{math},{\cal R}_{K-2},{\cal R}_{K-3},\ldots ,{\cal R}_{1},{\cal H}_{phys}\rbrace \,\) 
